关于BPS结构和Gopakumar-Vafa不变量的注解

IF 1.2 3区数学 Q1 MATHEMATICS

Communications in Number Theory and Physics Pub Date : 2018-12-18 DOI:10.4310/cntp.2019.v13.n3.a5

J. Stoppa

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引用次数: 5

摘要

我们考虑了Maulik和Toda的工作，提出了Gopakumar-Vafa不变量的sheaf理论方法，定义了BPS结构，即BPS不变量与中心电荷的集合。假设他们的猜想，我们证明了对应于这个BPS结构的平连接的规范平截面，在形式幂级数的水平上，再现了所有属的Gromov-Witten配分函数，直到属0和1中的一些误差项。这推广了Bridgeland和Iwaki对亏格0 Gopakumar-Vafa不变量的贡献的一个结果。

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A note on BPS structures and Gopakumar–Vafa invariants

We regard the work of Maulik and Toda, proposing a sheaf-theoretic approach to Gopakumar-Vafa invariants, as defining a BPS structure, that is, a collection of BPS invariants together with a central charge. Assuming their conjectures, we show that a canonical flat section of the flat connection corresponding to this BPS structure, at the level of formal power series, reproduces the Gromov-Witten partition function for all genera, up to some error terms in genus 0 and 1. This generalises a result of Bridgeland and Iwaki for the contribution from genus 0 Gopakumar-Vafa invariants.

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来源期刊

Communications in Number Theory and Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Focused on the applications of number theory in the broadest sense to theoretical physics. Offers a forum for communication among researchers in number theory and theoretical physics by publishing primarily research, review, and expository articles regarding the relationship and dynamics between the two fields.